/* ************************************************************************
 * Copyright (c) 2018 Advanced Micro Devices, Inc.
 *
 * Permission is hereby granted, free of charge, to any person obtaining a copy
 * of this software and associated documentation files (the "Software"), to deal
 * in the Software without restriction, including without limitation the rights
 * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
 * copies of the Software, and to permit persons to whom the Software is
 * furnished to do so, subject to the following conditions:
 *
 * The above copyright notice and this permission notice shall be included in
 * all copies or substantial portions of the Software.
 *
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
 * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
 * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
 * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
 * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
 * THE SOFTWARE.
 *
 * ************************************************************************ */

#include "../../utils/def.hpp"
#include "../../utils/types.hpp"
#include "idr.hpp"
#include "../iter_ctrl.hpp"

#include "../../base/local_matrix.hpp"
#include "../../base/local_stencil.hpp"
#include "../../base/local_vector.hpp"

#include "../../base/global_matrix.hpp"
#include "../../base/global_vector.hpp"

#include "../../base/matrix_formats_ind.hpp"

#include "../../utils/log.hpp"
#include "../../utils/allocate_free.hpp"
#include "../../utils/math_functions.hpp"

#include <math.h>
#include <time.h>

namespace rocalution {

template <class OperatorType, class VectorType, typename ValueType>
IDR<OperatorType, VectorType, ValueType>::IDR()
{
    log_debug(this, "IDR::IDR()", "default constructor");

    this->s_    = 4;
    this->seed_ = time(NULL);

    this->kappa_ = static_cast<ValueType>(0.7);

    this->c_ = NULL;
    this->f_ = NULL;
    this->M_ = NULL;

    this->G_ = NULL;
    this->U_ = NULL;
    this->P_ = NULL;
}

template <class OperatorType, class VectorType, typename ValueType>
IDR<OperatorType, VectorType, ValueType>::~IDR()
{
    log_debug(this, "IDR::~IDR()", "destructor");

    this->Clear();
}

template <class OperatorType, class VectorType, typename ValueType>
void IDR<OperatorType, VectorType, ValueType>::Print(void) const
{
    if(this->precond_ == NULL)
    {
        LOG_INFO("IDR(" << this->s_ << ") solver");
    }
    else
    {
        LOG_INFO("IDR(" << this->s_ << ") solver, with preconditioner:");
        this->precond_->Print();
    }
}

template <class OperatorType, class VectorType, typename ValueType>
void IDR<OperatorType, VectorType, ValueType>::PrintStart_(void) const
{
    if(this->precond_ == NULL)
    {
        LOG_INFO("IDR(" << this->s_ << ") (non-precond) linear solver starts");
    }
    else
    {
        LOG_INFO("PIDR(" << this->s_ << ") solver starts, with preconditioner:");
        this->precond_->Print();
    }
}

template <class OperatorType, class VectorType, typename ValueType>
void IDR<OperatorType, VectorType, ValueType>::PrintEnd_(void) const
{
    if(this->precond_ == NULL)
    {
        LOG_INFO("IDR(" << this->s_ << ") (non-precond) ends");
    }
    else
    {
        LOG_INFO("PIDR(" << this->s_ << ") ends");
    }
}

template <class OperatorType, class VectorType, typename ValueType>
void IDR<OperatorType, VectorType, ValueType>::Build(void)
{
    log_debug(this, "IDR::Build()", this->build_, " #*# begin");

    if(this->build_ == true)
    {
        this->Clear();
    }

    assert(this->build_ == false);
    assert(this->op_ != NULL);
    assert(this->op_->GetM() == this->op_->GetN());
    assert(this->op_->GetM() > 0);
    assert((IndexType2) this->s_ <= this->op_->GetM());

    this->r_.CloneBackend(*this->op_);
    this->v_.CloneBackend(*this->op_);

    this->r_.Allocate("r", this->op_->GetM());
    this->v_.Allocate("v", this->op_->GetM());

    allocate_host(this->s_, &this->c_);
    allocate_host(this->s_, &this->f_);
    allocate_host(this->s_ * this->s_, &this->M_);

    this->G_ = new VectorType*[this->s_];
    this->U_ = new VectorType*[this->s_];
    this->P_ = new VectorType*[this->s_];

    for(int i = 0; i < this->s_; ++i)
    {
        this->G_[i] = new VectorType;
        this->U_[i] = new VectorType;
        this->P_[i] = new VectorType;

        this->G_[i]->CloneBackend(*this->op_);
        this->U_[i]->CloneBackend(*this->op_);
        this->P_[i]->CloneBackend(*this->op_);

        this->G_[i]->Allocate("g", this->op_->GetM());
        this->U_[i]->Allocate("u", this->op_->GetM());
        this->P_[i]->Allocate("P", this->op_->GetM());

        this->P_[i]->SetRandomNormal((i + 1) * this->seed_, 0.0, 1.0);
    }

    if(this->precond_ != NULL)
    {
        this->precond_->SetOperator(*this->op_);

        this->precond_->Build();

        this->t_.CloneBackend(*this->op_);
        this->t_.Allocate("t", this->op_->GetM());
    }

    // Build ONB out of P using modified Gram-Schmidt algorithm
    for(int k = 0; k < this->s_; ++k)
    {
        for(int j = 0; j < k; ++j)
        {
            this->P_[k]->AddScale(*this->P_[j], -this->P_[j]->Dot(*this->P_[k]));
        }
        this->P_[k]->Scale(static_cast<ValueType>(1) / this->P_[k]->Norm());
    }

    this->build_ = true;

    log_debug(this, "IDR::Build()", this->build_, " #*# end");
}

template <class OperatorType, class VectorType, typename ValueType>
void IDR<OperatorType, VectorType, ValueType>::Clear(void)
{
    log_debug(this, "IDR::Clear()", this->build_);

    if(this->build_ == true)
    {
        this->r_.Clear();
        this->v_.Clear();

        for(int i = 0; i < this->s_; ++i)
        {
            delete this->U_[i];
            delete this->G_[i];
            delete this->P_[i];
        }

        delete[] this->U_;
        delete[] this->G_;
        delete[] this->P_;

        this->U_ = NULL;
        this->G_ = NULL;
        this->P_ = NULL;

        free_host(&this->c_);
        free_host(&this->f_);
        free_host(&this->M_);

        if(this->precond_ != NULL)
        {
            this->precond_->Clear();
            this->precond_ = NULL;

            this->t_.Clear();
        }

        this->iter_ctrl_.Clear();

        this->build_ = false;
    }
}

template <class OperatorType, class VectorType, typename ValueType>
void IDR<OperatorType, VectorType, ValueType>::ReBuildNumeric(void)
{
    log_debug(this, "IDR::ReBuildNumeric()", this->build_);

    if(this->build_ == true)
    {
        this->r_.Zeros();
        this->v_.Zeros();

        for(int i = 0; i < this->s_; ++i)
        {
            this->U_[i]->Zeros();
            this->G_[i]->Zeros();
            this->P_[i]->Zeros();
        }

        if(this->precond_ != NULL)
        {
            this->precond_->ReBuildNumeric();
            this->t_.Zeros();
        }

        this->iter_ctrl_.Clear();
    }
    else
    {
        this->Build();
    }
}

template <class OperatorType, class VectorType, typename ValueType>
void IDR<OperatorType, VectorType, ValueType>::SetShadowSpace(int s)
{
    log_debug(this, "IDR:SetShadowSpace()", s);

    assert(this->build_ == false);
    assert(s > 0);
    assert(this->op_ != NULL);
    assert((IndexType2)s <= this->op_->GetM());

    this->s_ = s;
}

template <class OperatorType, class VectorType, typename ValueType>
void IDR<OperatorType, VectorType, ValueType>::SetRandomSeed(unsigned long long seed)
{
    log_debug(this, "IDR::SetRandomSeed()", seed);

    assert(this->build_ == false);
    assert(seed > 0ULL);

    this->seed_ = seed;
}

template <class OperatorType, class VectorType, typename ValueType>
void IDR<OperatorType, VectorType, ValueType>::MoveToHostLocalData_(void)
{
    log_debug(this, "IDR::MoveToHostLocalData_()", this->build_);

    if(this->build_ == true)
    {
        this->r_.MoveToHost();
        this->v_.MoveToHost();

        for(int i = 0; i < this->s_; ++i)
        {
            this->U_[i]->MoveToHost();
            this->G_[i]->MoveToHost();
            this->P_[i]->MoveToHost();
        }

        if(this->precond_ != NULL)
        {
            this->t_.MoveToHost();
        }
    }
}

template <class OperatorType, class VectorType, typename ValueType>
void IDR<OperatorType, VectorType, ValueType>::MoveToAcceleratorLocalData_(void)
{
    log_debug(this, "IDR::MoveToAcceleratorLocalData_()", this->build_);

    if(this->build_ == true)
    {
        this->r_.MoveToAccelerator();
        this->v_.MoveToAccelerator();

        for(int i = 0; i < this->s_; ++i)
        {
            this->U_[i]->MoveToAccelerator();
            this->G_[i]->MoveToAccelerator();
            this->P_[i]->MoveToAccelerator();
        }

        if(this->precond_ != NULL)
        {
            this->t_.MoveToAccelerator();
        }
    }
}

template <class OperatorType, class VectorType, typename ValueType>
void IDR<OperatorType, VectorType, ValueType>::SolveNonPrecond_(const VectorType& rhs,
                                                                VectorType* x)
{
    log_debug(this, "IDR::SolveNonPrecond_()", " #*# begin", (const void*&)rhs, x);

    assert(x != NULL);
    assert(x != &rhs);
    assert(this->op_ != NULL);
    assert(this->precond_ == NULL);
    assert(this->build_ == true);

    const OperatorType* op = this->op_;

    VectorType* r  = &this->r_;
    VectorType* v  = &this->v_;
    VectorType** G = this->G_;
    VectorType** U = this->U_;
    VectorType** P = this->P_;

    int s           = this->s_;
    ValueType zero  = static_cast<ValueType>(0);
    ValueType one   = static_cast<ValueType>(1);
    ValueType kappa = this->kappa_;

    ValueType* c = this->c_;
    ValueType* f = this->f_;
    ValueType* M = this->M_;

    ValueType alpha;
    ValueType beta;
    ValueType rho;
    ValueType omega = one;

    // Initial residual r = b - Ax
    op->Apply(*x, r);
    r->ScaleAdd(-one, rhs);

    // use for |b-Ax0|
    ValueType res_norm = this->Norm_(*r);

    if(this->iter_ctrl_.InitResidual(rocalution_abs(res_norm)) == false)
    {
        log_debug(this, "::SolvePrecond_()", " #*# end");
        return;
    }

    // G = U = 0
    for(int i = 0; i < s; ++i)
    {
        G[i]->Zeros();
        U[i]->Zeros();

        for(int j = 0; j < s; ++j)
        {
            M[DENSE_IND(i, j, s, s)] = (i == j) ? one : zero;
        }
    }

    // IDR(s) iteration
    while(true)
    {
        // Generate rhs for small system
        // f = P^T * r
        for(int i = 0; i < s; ++i)
        {
            f[i] = P[i]->Dot(*r);
        }

        // Loop over shadow spaces
        for(int k = 0; k < s; ++k)
        {
            // v = r
            v->CopyFrom(*r);

            // Solve lower triangular system Mc = f
            for(int i = k; i < s; ++i)
            {
                c[i] = f[i];

                for(int j = k; j < i; ++j)
                {
                    c[i] -= M[DENSE_IND(i, j, s, s)] * c[j];
                }

                c[i] /= M[DENSE_IND(i, i, s, s)];
                v->AddScale(*G[i], -c[i]);
            }

            // U_k = omega * v + sum(c_i * U_i), i=k,...,s-1
            U[k]->ScaleAddScale(c[k], *v, omega);

            for(int i = k + 1; i < s; ++i)
            {
                U[k]->AddScale(*U[i], c[i]);
            }

            // G_k = A U_k
            op->Apply(*U[k], G[k]);

            // Make G orthogonal to P
            for(int i = 0; i < k; ++i)
            {
                // alpha = P^T_i * G_k / M_ii
                alpha = P[i]->Dot(*G[k]) / M[DENSE_IND(i, i, s, s)];

                // G_k = G_k - alpha * G_i
                G[k]->AddScale(*G[i], -alpha);

                // U_k = U_k - alpha * U_i
                U[k]->AddScale(*U[i], -alpha);
            }

            // Update column k of M
            for(int i = k; i < s; ++i)
            {
                // M_ik = P^T_i * G_k
                M[DENSE_IND(i, k, s, s)] = P[i]->Dot(*G[k]);
            }

            // Check M_kk for zero
            if(M[DENSE_IND(k, k, s, s)] == zero)
            {
                LOG_INFO("IDR(s) break down ; M(k,k) == 0.0");
                FATAL_ERROR(__FILE__, __LINE__);
            }

            // Check M_kk for NaN
            if(M[DENSE_IND(k, k, s, s)] != M[DENSE_IND(k, k, s, s)])
            {
                LOG_INFO("IDR(s) break down ; M(k,k) == NaN");
                FATAL_ERROR(__FILE__, __LINE__);
            }

            // Check M_kk for zero
            if(M[DENSE_IND(k, k, s, s)] == std::numeric_limits<ValueType>::infinity())
            {
                LOG_INFO("IDR(s) break down ; M(k,k) == inf");
                FATAL_ERROR(__FILE__, __LINE__);
            }

            // Make residual r orthogonal to P

            // beta = f_k / M_k_k
            beta = f[k] / M[DENSE_IND(k, k, s, s)];

            // r = r - beta * G_k
            r->AddScale(*G[k], -beta);

            // x = x + beta * U_k
            x->AddScale(*U[k], beta);

            // Residual norm
            res_norm = this->Norm_(*r);

            // Check inner loop for convergence
            if(this->iter_ctrl_.CheckResidualNoCount(rocalution_abs(res_norm)))
            {
                break;
            }

            // f_i = f_i - beta * M_ik
            for(int i = k + 1; i < s; ++i)
            {
                f[i] -= beta * M[DENSE_IND(i, k, s, s)];
            }
        }

        // Check convergence
        if(this->iter_ctrl_.CheckResidual(rocalution_abs(res_norm), this->index_))
        {
            break;
        }

        // Enter the dimension reduction step

        // v = Ar
        op->Apply(*r, v);

        // omega = (v,r) / ||v||^2
        ValueType rt = v->Dot(*r);
        ValueType nt = v->Norm();

        rt /= nt;

        rho   = rocalution_abs(rt / res_norm);
        omega = rt / nt;

        if(rho < kappa)
        {
            omega *= kappa / rho;
        }

        // Check omega for zero
        if(omega == zero)
        {
            LOG_INFO("IDR(s) break down ; w == 0.0");
            FATAL_ERROR(__FILE__, __LINE__);
        }

        // Check omega for NaN
        if(omega != omega)
        {
            LOG_INFO("IDR(s) break down ; w == NaN");
            FATAL_ERROR(__FILE__, __LINE__);
        }

        // Check omega for inf
        if(omega == std::numeric_limits<ValueType>::infinity())
        {
            LOG_INFO("IDR(s) break down ; w == inf");
            FATAL_ERROR(__FILE__, __LINE__);
        }

        // x = x + omega * r
        x->AddScale(*r, omega);

        // r = r - omega * v
        r->AddScale(*v, -omega);

        // Residual norm to check outer loop convergence
        res_norm = this->Norm_(*r);
    }

    log_debug(this, "IDR::SolveNonPrecond_()", " #*# end");
}

template <class OperatorType, class VectorType, typename ValueType>
void IDR<OperatorType, VectorType, ValueType>::SolvePrecond_(const VectorType& rhs, VectorType* x)
{
    log_debug(this, "IDR::SolvePrecond_()", " #*# begin", (const void*&)rhs, x);

    assert(x != NULL);
    assert(x != &rhs);
    assert(this->op_ != NULL);
    assert(this->precond_ != NULL);
    assert(this->build_ == true);

    const OperatorType* op = this->op_;

    VectorType* r  = &this->r_;
    VectorType* v  = &this->v_;
    VectorType* t  = &this->t_;
    VectorType** G = this->G_;
    VectorType** U = this->U_;
    VectorType** P = this->P_;

    int s           = this->s_;
    ValueType zero  = static_cast<ValueType>(0);
    ValueType one   = static_cast<ValueType>(1);
    ValueType kappa = this->kappa_;

    ValueType* c = this->c_;
    ValueType* f = this->f_;
    ValueType* M = this->M_;

    ValueType alpha;
    ValueType beta;
    ValueType rho;
    ValueType omega = one;

    // Initial residual r = b - Ax
    op->Apply(*x, r);
    r->ScaleAdd(-one, rhs);

    // use for |b-Ax0|
    ValueType res_norm = this->Norm_(*r);

    if(this->iter_ctrl_.InitResidual(rocalution_abs(res_norm)) == false)
    {
        log_debug(this, "::SolvePrecond_()", " #*# end");
        return;
    }

    // G = U = 0
    for(int i = 0; i < s; ++i)
    {
        G[i]->Zeros();
        U[i]->Zeros();

        for(int j = 0; j < s; ++j)
        {
            M[DENSE_IND(i, j, s, s)] = (i == j) ? one : zero;
        }
    }

    // IDR(s) iteration
    while(true)
    {
        // Generate rhs for small system
        // f = P^T * r
        for(int i = 0; i < s; ++i)
        {
            f[i] = P[i]->Dot(*r);
        }

        // Loop over shadow spaces
        for(int k = 0; k < s; ++k)
        {
            // v = r
            v->CopyFrom(*r);

            // Solve lower triangular system Mc = f
            for(int i = k; i < s; ++i)
            {
                c[i] = f[i];

                for(int j = k; j < i; ++j)
                {
                    c[i] -= M[DENSE_IND(i, j, s, s)] * c[j];
                }

                c[i] /= M[DENSE_IND(i, i, s, s)];
                v->AddScale(*G[i], -c[i]);
            }

            // Apply preconditioner Mt = v
            this->precond_->SolveZeroSol(*v, t);

            // U_k = omega * t + sum(c_i * U_i), i=k,...,s-1
            U[k]->ScaleAddScale(c[k], *t, omega);

            for(int i = k + 1; i < s; ++i)
            {
                U[k]->AddScale(*U[i], c[i]);
            }

            // G_k = A U_k
            op->Apply(*U[k], G[k]);

            // Make G orthogonal to P
            for(int i = 0; i < k; ++i)
            {
                // alpha = P^T_i * G_k / M_ii
                alpha = P[i]->Dot(*G[k]) / M[DENSE_IND(i, i, s, s)];

                // G_k = G_k - alpha * G_i
                G[k]->AddScale(*G[i], -alpha);

                // U_k = U_k - alpha * U_i
                U[k]->AddScale(*U[i], -alpha);
            }

            // Update column k of M
            for(int i = k; i < s; ++i)
            {
                // M_ik = P^T_i * G_k
                M[DENSE_IND(i, k, s, s)] = P[i]->Dot(*G[k]);
            }

            // Check M_kk for zero
            if(M[DENSE_IND(k, k, s, s)] == zero)
            {
                LOG_INFO("IDR(s) break down ; M(k,k) == 0.0");
                FATAL_ERROR(__FILE__, __LINE__);
            }

            // Check M_kk for NaN
            if(M[DENSE_IND(k, k, s, s)] != M[DENSE_IND(k, k, s, s)])
            {
                LOG_INFO("IDR(s) break down ; M(k,k) == NaN");
                FATAL_ERROR(__FILE__, __LINE__);
            }

            // Check M_kk for zero
            if(M[DENSE_IND(k, k, s, s)] == std::numeric_limits<ValueType>::infinity())
            {
                LOG_INFO("IDR(s) break down ; M(k,k) == inf");
                FATAL_ERROR(__FILE__, __LINE__);
            }

            // Make residual r orthogonal to P

            // beta = f_k / M_k_k
            beta = f[k] / M[DENSE_IND(k, k, s, s)];

            // r = r - beta * G_k
            r->AddScale(*G[k], -beta);

            // x = x + beta * U_k
            x->AddScale(*U[k], beta);

            // Residual norm
            res_norm = this->Norm_(*r);

            // Check inner loop for convergence
            if(this->iter_ctrl_.CheckResidualNoCount(rocalution_abs(res_norm)))
            {
                break;
            }

            // f_i = f_i - beta * M_ik
            for(int i = k + 1; i < s; ++i)
            {
                f[i] -= beta * M[DENSE_IND(i, k, s, s)];
            }
        }

        // Check convergence
        if(this->iter_ctrl_.CheckResidual(rocalution_abs(res_norm), this->index_))
        {
            break;
        }

        // Enter the dimension reduction step

        // Mv = r
        this->precond_->SolveZeroSol(*r, v);

        // t = Av
        op->Apply(*v, t);

        // omega = (t,r) / ||t||^2
        ValueType rt = t->Dot(*r);
        ValueType nt = t->Norm();

        rt /= nt;

        rho   = rocalution_abs(rt / res_norm);
        omega = rt / nt;

        if(rho < kappa)
        {
            omega *= kappa / rho;
        }

        // Check omega for zero
        if(omega == zero)
        {
            LOG_INFO("IDR(s) break down ; w == 0.0");
            FATAL_ERROR(__FILE__, __LINE__);
        }

        // Check omega for NaN
        if(omega != omega)
        {
            LOG_INFO("IDR(s) break down ; w == NaN");
            FATAL_ERROR(__FILE__, __LINE__);
        }

        // Check omega for inf
        if(omega == std::numeric_limits<ValueType>::infinity())
        {
            LOG_INFO("IDR(s) break down ; w == inf");
            FATAL_ERROR(__FILE__, __LINE__);
        }

        // r = r - omega * t
        r->AddScale(*t, -omega);

        // x = x + omega * v
        x->AddScale(*v, omega);

        // Residual norm to check outer loop convergence
        res_norm = this->Norm_(*r);
    }

    log_debug(this, "::SolvePrecond_()", " #*# end");
}

template class IDR<LocalMatrix<double>, LocalVector<double>, double>;
template class IDR<LocalMatrix<float>, LocalVector<float>, float>;
#ifdef SUPPORT_COMPLEX
template class IDR<LocalMatrix<std::complex<double>>,
                   LocalVector<std::complex<double>>,
                   std::complex<double>>;
template class IDR<LocalMatrix<std::complex<float>>,
                   LocalVector<std::complex<float>>,
                   std::complex<float>>;
#endif

template class IDR<GlobalMatrix<double>, GlobalVector<double>, double>;
template class IDR<GlobalMatrix<float>, GlobalVector<float>, float>;
#ifdef SUPPORT_COMPLEX
template class IDR<GlobalMatrix<std::complex<double>>,
                   GlobalVector<std::complex<double>>,
                   std::complex<double>>;
template class IDR<GlobalMatrix<std::complex<float>>,
                   GlobalVector<std::complex<float>>,
                   std::complex<float>>;
#endif

template class IDR<LocalStencil<double>, LocalVector<double>, double>;
template class IDR<LocalStencil<float>, LocalVector<float>, float>;
#ifdef SUPPORT_COMPLEX
template class IDR<LocalStencil<std::complex<double>>,
                   LocalVector<std::complex<double>>,
                   std::complex<double>>;
template class IDR<LocalStencil<std::complex<float>>,
                   LocalVector<std::complex<float>>,
                   std::complex<float>>;
#endif

} // namespace rocalution
